Special 24

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
Age
7 to 11
Challenge level
filled star filled star empty star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative


Special 24

 The number $24$ is special because it is just one short of being a square number.

 So $24 + 1 = 25$ and $5^2 = 25$

 AND when you double $24$ the answer is also one short of being a square

 number.

So $24 \times 2 = 48$ and $48 + 1 = 49$ and $7^2 = 49$.

Find another number that is special in the same way as $24$.